2008/11/01 by Alexander Goldenshluger, Oleg Lepski · 1 citation
Economics, Econometrics and Finance · Mathematics · #Advanced Statistical Methods and Models #Financial Risk and Volatility Modeling #Statistical Methods and Inference #math.ST #stat.TH
paper · pdf · doi:10.3150/08-bej144
published as Bernoulli 2008, Vol. 14, No. 4, 1150-1190 · Published in at http://dx.doi.org/10.3150/08-BEJ144 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
openalex publication_date 2008/11/01 · arxiv created 2008/11/17 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper, we study the problem of pointwise estimation of a multivariate function. We develop a general pointwise estimation procedure that is based on selection of estimators from a large parameterized collection. An upper bound on the pointwise risk is established and it is shown that the proposed selection procedure specialized for different collections of estimators leads to minimax and adaptive minimax estimators in various settings.